Transition to First Frame of Fluid Sim
Thanks to @Jbergman for the answer (see comments for additional details).

The main problem was that I had a concave "saucer" obstacle under the fluid, hoping that it would keep the fluid from pooling against the sides of the domain.  The fluid wasn't technically touching the saucer mesh, but I had the saucer's Volume Initialization set to Volume.  This caused the simulator to include the concave volume in the obstacle.  Setting it to Shell fixed it (using a closed mesh as the obstacle may have fixed it also, but I didn't try this).  [Since the saucer was invisible, no one could have found the problem without the original blend file; sorry about that.]

A few other points that he reminded me of:


The domain was much bigger than it needed to be.  Making it smaller
allowed me to use a higher resolution.
I didn't apply the scale to the domain; apparently this can cause
other odd behavior.
The resolution is going to limit how close the first frame looks to
the original mesh.  It's close enough now that I can just copy the
first frame of the domain mesh and use it for the first 24 animation
frames, instead of the original mesh.  If I was really ambitious, I
think could edit this domain copy to look more like the original and
use shape keys for a smooth pre-sim transition, as discussed in the
comments.


Below is how the first frame looks now: